For my petition drive, I requested formal proposals from several profession petition-gathering firms and got 3. Here links to the firms I was able to find on the web:
In the proposals I received, the approach was to set up offices in major cities like Detroit, Grand Rapids and Lansing. Petitions circulators would be recruited - there are a lot of "regulars" out there who've worked on several drives, even traveling from state to state - and trained. The circulators would bring the completed petitions back to the office where they'd get a paycheck based on the number of signatures collected. They'd also get critiqued on the quality of their work, and if too many of their signatures were invalid, they'd get fired.
Most of the firms had computer systems they used to verify that signatures were of registered voters. Some verified only a sampling of signatures, but some - for an extra fee - would verify every one. And some will, at the end of the petition drive, provide a list of all signers that you can use to use in promoting your ballot proposal.
From the start of my petition drive, I planned on paying circulators, but I planned to run the operation myself (with my paid staff) rather than contracting with a signature-gathering firm. (Later, I decided that I'd have better luck attracting financial backers if I used professionals.) My approach to the project was different from how the professionals do it. I planned to do everything by mail. Circulators would be recruited using a form on my website. Packages of petition forms would be mailed along with instructions and a postage-paid return envelope. When the package was returned, the signatures would be verified using a copy of the Qualified Voter File and checks would be mailed to the circulators, paying only for valid signatures. The advantage to my system was that anybody anywhere in the state could be a circulator, and they'd never have to travel to an office. Also, interference from initiative opponents - unions, in this instance - would be less if circulators were not concentrated around a few cities and could not be observed entering or leaving our office. And only one office, or processing center, would be needed, and its location could be anywhere.